In this paper, we consider a distributed remote source coding problem, where
a sequence of observations of source vectors is available at the encoder. The
problem is to specify the optimal rate for encoding the observations subject to
a covariance matrix distortion constraint and in the presence of side
information at the decoder. For this problem, we derive lower and upper bounds
on the rate-distortion function (RDF) for the Gaussian case, which in general
do not coincide. We then provide some cases, where the RDF can be derived
exactly. We also show that previous results on specific instances of this
problem can be generalized using our results. We finally show that if the
distortion measure is the mean squared error, or if it is replaced by a certain
mutual information constraint, the optimal rate can be derived from our main
result.Comment: This is the final version accepted at ISIT'1
